Learner-generated graphic representations for word problems: an intervention and evaluation study in grade 3
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Learner-generated graphic representations for word problems: an intervention and evaluation study in grade 3 Barbara Ott 1 Published online: 3 September 2020 # The Author(s) 2020
Abstract
The use of written or graphic representations is essential in mathematics. Graphic representations are mainly used and researched as instruments for problem solving. There is a gap in research for interventions that use learner-generated graphic representations as documents for reflection processes for promoting the development of children’s graphic representation competences. This is the focus of the study presented here. The study examines to what extent such an intervention has an effect on how the children take into account a mathematical structure in their self-generated graphic representations, how they ensure a mathematical matching with the word problem, and what degree of abstraction they choose. Additionally, the effect on the solution rates is investigated. The results show that children in the intervention group more frequently pay attention to a mathematically appropriate structure, compared with children in the control groups. This result is statistically significant. At the same time, children keep the degree of abstraction relatively constant. Solution rates improve continuously, but the difference is not significant. Keywords Inscriptions . Graphic representations . Word problems . Reflection . Intervention study
1 Introduction In the practice of mathematics, the use of inscriptions, i.e., representations that exist in material form (Roth & McGinn, 1998), is essential. Without such material representations, it is virtually impossible to acquire a mathematical understanding (Dörfler, 2008; Goldin & Shteingold, 2001). Accordingly, representation is now normatively set as a mathematical competence in the standards and curricula of many countries (e.g., NCTM, 2000). This competence is often * Barbara Ott [email protected]
1
St. Gallen University of Teacher Education, Notkerstrasse 27, 9000 St. Gallen, Switzerland
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Ott B.
associated with problem solving. Furthermore, in research, the flexible and adaptive use of different representations is considered essential for mathematical problem solving (Heinze, Star, & Verschaffel, 2009). The generation of a graphic representation is regarded as an important heuristic (Hembree, 1992). At the same time, it is often reported that many learners rarely use graphic representations as heuristics (Fagnant & Vlassis, 2013; Lopez Real & Veloo, 1993). This is particularly evident at the primary school level, where interventions involving graphic representations for problem solving often have almost no positive effects (Hembree, 1992). Thus, a tension between mathematically and didactically motivated ideas on the one hand and the use by learners at the primary school level on the other hand becomes apparent. In intervention studies, graphic representations are mostly examined as instruments for problem solving (e.g., Van Essen & Hamaker, 1990). There is a gap in the research on
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